In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very strong monotonicity properties...

{\displaystyle g:\mathbb {R} \to \mathbb {R} } be a monotonic function, then the resulting density function is f Y ( y ) = f X ( g − 1 ( y ) ) | d d y ( g...

well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson...

}\left(1\wedge x\right)\mu (dx)<\infty .} Absolutely and completely monotonic functions and sequences S. N. Bernstein (1928). "Sur les fonctions absolument...

Absolutely and completely monotonic functions and sequences Levin, Vladimir (1 March 1999). "Abstract Cyclical Monotonicity and Monge Solutions for the...

object Monotonic function, a property of a mathematical function Monotonicity of entailment, a property of some logical systems Monotonically increasing...

inputs. Strict monotonic function: preserves the given order. Real function: a function whose domain is real. Complex function: a function whose domain...

determined by reverse look up in the same table, since the logarithm is a monotonic function. The product and quotient of two positive numbers c and d were routinely...

be a complete lattice and let f : L → L be an order-preserving (monotonic) function w.r.t. ≤. Then the set of fixed points of f in L forms a complete...

mathematical functions Injective metric space – Type of metric space Monotonic function – Order-preserving mathematical function Univalent function – Mathematical...

sequence. This is a special case of the more general notion of a monotonic function. The terms nondecreasing and nonincreasing are often used in place...

concave function can be quasiconvex. For example, x ↦ log ⁡ ( x ) {\displaystyle x\mapsto \log(x)} is both concave and quasiconvex. Any monotonic function is...

trigonometric function is monotonic, one can define an inverse function, and this defines inverse trigonometric functions as multivalued functions. To define...

square function preserves the order of positive numbers: larger numbers have larger squares. In other words, the square is a monotonic function on the...

value zero for x = 1, is a differentiable function called the natural logarithm. A real function f is monotonic in an interval if the sign of f ( x ) −...

temperature ranges (negative thermal expansion). Temperature is a monotonic function of the average molecular kinetic energy of a substance. As energy...

has a positive derivative at each point. In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the...

internal isotopic equilibrium are predicted and verified to vary as monotonic functions of temperature of equilibration as follows: Δ 18 = − 0.0117 ( 10...

MR 2356043. Gelbaum, Bernard R.; Olmsted, John M. H. (1964), "18: A monotonic function whose points of discontinuity form an arbitrary countable (possibly...

since it allows convex analysis to be used. Since squaring is a monotonic function of non-negative values, minimizing squared distance is equivalent...

different orthographies: el-monoton for monotonic Greek. el-polyton for polytonic Greek. While the tónos of monotonic orthography looks similar to the oxeîa...

Examples of non-monotonic queries are aggregation queries, or queries with set difference. Identifying whether a query is monotonic can be crucial for...

well the relationship between two variables can be described by a monotonic function. The Kendall tau rank correlation coefficient is a measure of the...

arc length s is a differentiable monotonic function of the parameter t, and conversely that t is a monotonic function of s. Moreover, by changing, if needed...

and equivalence and often occurs in the context of inequality and monotonic functions. It is often attached to a technical term to indicate that the exclusive...

{\displaystyle [\mathbf {x} ]} . Interval functions beyond the four basic operators may also be defined. For monotonic functions in one variable, the range of values...

model Multinomial probit Q–Q plot Continuous function Monotonic function Quantile function Sigmoid function Rankit analysis, also developed by Chester Bliss...

cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,...

x^{6}(1-x)^{4}d\mu (x)\geq 0.} Absolutely and completely monotonic functions and sequences Total monotonicity Hausdorff, F. "Summationsmethoden und Momentfolgen...